Structure of Sodium Carboxymethyl Cellulose Aqueous Solutions: a SANS and Rheology Study

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Structure of Sodium Carboxymethyl Cellulose Aqueous Solutions: A SANS and Rheology Study

Carlos G. Lopez,1 Sarah E. Rogers,2 Ralph H. Colby,3 Peter Graham,4 Joao~ T. Cabral1 1Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom 2Diffraction and Materials Division, ISIS-STFC, Rutherford Appleton Laboratory, Chilton, Oxon OX11 0QX, United Kingdom 3Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802 4Unilever Research Port Sunlight Laboratory, Quarry Road East, Bebington L63 3JW, United Kingdom Correspondence to: J. T. Cabral (E-mail: [email protected])

Received 11 August 2014; revised 2 December 2014; accepted 5 December 2014; published online 30 December 2014 DOI: 10.1002/polb.23657

ABSTRACT: We report a small angle neutron scattering (SANS) ing semidilute unentangled and entangled regimes, followed and rheology study of cellulose derivative polyelectrolyte by what appears to be a crossover to neutral polymer concen- sodium carboxymethyl cellulose with a degree of substitution tration dependence of viscosity at high concentrations. Yet of 1.2. Using SANS, we establish that this polymer is molecu- those higher concentrations, in the concentrated regime larly dissolved in water with a locally stiff conformation with a defined by rheology, still exhibit a peak in the scattering func- stretching parameter B ’ 1:06. We determine the cross section that indicates a correlation length that continues to scale 21=2 tional radius of the chain (rp ’ 3.4 A˚ ) and the scaling of as c . VC 2014 The Authors. Journal of Polymer Science Part the correlation length with concentration (n 5 296 c21=2A˚ for c B: Polymer Physics Published by Wiley Periodicals, Inc. in g/L) is found to remain unchanged from the semidilute to J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 492–501 concentrated crossover as identified by rheology. Viscosity measurements are found to be in qualitative agreement with KEYWORDS: polyelectrolytes; cellulose; neutron scattering; rhe- scaling theory predictions for flexible polyelectrolytes exhibit- ology; structural characterization; water-soluble polymers

7 INTRODUCTION tile treatments and to prevent the redeposition of soil removed by detergents during the fabric washing process.8 Its Cellulose and Cellulose Derivatives monomer structure is shown in Figure 1, where R stands for Cellulose is the most abundant polymer on Earth with annual AHorACH CO Na. The degree of substitution (D.S.) is the cellulose synthesis by plants approaching 1012 tons.1 Although 2 2 average number of carboxymethyl groups substituted per cellulose is insoluble in water and most common organic sol- monomer unit, ranging from 0 to 3 with the remaining R 5 H. vents,2 cellulose derivatives are soluble in a wide range of sol- 3 vents; for example, cellulose acetate is soluble in acetone, Aqueous solutions of NaCMC are generally complex. Some stud- tetrahydrofuran, and other organic solvents while methylcellu- 9,10 ies suggest that only a fraction is molecularly dispersed, lose, ethyl hydroxyethyl cellulose, and sodium carboxymethyl implying that NaCMC is a colloidally dispersed polymer while cellulose (NaCMC) are water soluble.2,4 Cellulose derivatives others report full solubility in dilute salt solutions.11,12 The can be dissolved either at a molecular or colloidal level.2,3 degree of solubility is accepted to be a function of the degree of Carboxymethylcellulose (CMC), generally used as sodium salt substitution, with less substituted (more hydrophobic) NaCMC 10 NaCMC, is one of the most widely used polyelectrolyte cellu- showing a larger fraction of aggregates. Aggregated crystalline lose derivatives.5 NaCMC is an anionic, water soluble, polyelec- domains have been found by X-ray diffraction in aqueous solu- 13 trolyte with vast applications in the food, pharmaceutical, tion, with degree of crystallinity correlating with lower D.S. and personal care/cosmetic, paper and other industries.4 For no crystallinity found for D.S. 1.06. Additionally, low substitu- instance, NaCMC is extensively used as a rheology modifier in tion grades often exhibit thixotropy10,14 which is thought to common toothpastes and shampoos,6 as a film former in tex- result from the formation of networks or soft aggregates.10 The

Additional Supporting Information may be found in the online version of this article.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

VC 2014 The Authors. Journal of Polymer Science Part B: Polymer Physics Published by Wiley Periodicals, Inc.

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BACKGROUND THEORY

Scaling Theory e2 The Bjerrum length lB5 , where e is the unit of charge, 4p0kBT 0 is the vacuum permitivity, is the relative dielectric constant, and kB is the Boltzmann constant, is defined as the distance at which the electrostatic energy between two FIGURE 1 Monomer structure of sodium NaCMC, where R can charges is equal to the thermal energy (7.1 Å for water at be H or CH COONa. The degree of substitution (D.S.) is defined 2 25 C). Salt free solutions of flexible polyelectrolytes can be as the average number of CH COONa groups per monomer 2 classified into dilute, semidilute (non entangled and out of a maximum of 3. [Color figure can be viewed in the entangled), and concentrated. In dilute solutions, c < c*, online issue, which is available at wileyonlinelibrary.com.] where c* is the overlap concentration, polyelectrolytes adopt an extended conformation and can be represented by a

directed random walk of electrostatic blobs of diameter nT. regularity of monomer substitution, instead of the average D.S., ( 2 1=3 was found to be the main factor controlling the rheological prop- bðA b=lBÞ ; T h erties of NaCMC aqueous solutions.10 NaCMC of low D.S. but uni- nT 5 (1) b A2b=l 3=7; T h form substitution, that is, lacking blocks of unsubstituted ð BÞ monomers, yields similar properties to highly substituted grades. where A is the number of monomers per effectively charged Typically, samples with D.S. տ 1, do not exhibit thixotropy as, group, h is the theta temperature, and b is the monomer length. with increasing D.S., substitution becomes more random. For this For distances below nT, thermal energy dominates and the chain study, we have selected a sample of D.S. ’ 1.2 and, therefore, conformation depends on the solvent quality, becoming extended expect no significant blocks of unsubstituted cellulose, and thus in good solvent and collapsed in poor solvent. The stretching no thixotropy or gelling at high concentrations. According to a parameter (B5bgT =nT ), where gT is the number of monomers in 15,16 model by Reuben et al., for an average D.S. 5 1.2, 10–20% of an electrostatic blob, is defined as the ratio between the polymer the monomers will not be substituted and thus, even in the contour length L 5 Nb,whereN isthedegreeofpolymerization, absence of large unsubstituted blocks, hydrophobic interactions and the end-to-end length in dilute solution, Ree 5 NnT =gT .The from unsubstituted monomers remain. A range of intrinsic per- scaling prediction for the specific viscosity at zero shear rate sistence lengths (l ) for NaCMC have been reported, varying g02gs 0 (gsp g ,whereg0 is the dynamic viscosity at zero shear rate 11,17,18 s from 5 to 15 nm characteristic of a semiflexible polymer and gs is the solvent’s dynamic viscosity) in dilute solution is gsp 18,19 and typical of many polysaccharides. c=c . Throughout this article, we use gsp to refer to the specific viscosity in the Newtonian (zero shear rate) limit. The rheology of NaCMC in aqueous, salt free, solutions has been previously studied.5,10,14,20–24 A Fuoss or near Fuoss depend- At c*, estimated by 1=2 ence of the specific viscosity (gsp / c ) has been reported in 20–22,24 the semidilute unentangled regime. Astrongdepend- N c ’ 5B3b23N22 (2) ence of the specific viscosity (gsp) with polymer concentration R3 3:7525:5 20,24 ee (gsp / c ) is reported at high concentration. chains begin to overlap. In the semidilute regime, the most rele- 25 Simulations by Wang and Somasundaran suggest that vant length scale is now the correlation length n;atlength NaCMC adopts a helical conformation in bulk and in solution scales smaller than n, chains do not interact and the conforma- 26 while Biermann et al. found that, depending on the tion is like that of a dilute solution; at length scales larger than substitution pattern, the chain may be locally collapsed or n, the electrostatic energy is screened and chains follow random highly extended. Although a helical chain conformation is coil statistics. A peak in the structure factor, S(q), is observed in suggested by optical rotary dispersion and circular flexible semidilute salt free polyelectrolytes, whose position 27–29 dichroism data, light scattering, intrinsic viscosity, scales as q / c1=2, in agreement with the scaling prediction: potentiometric titration, and dielectric spectroscopy data have been successfully interpreted assuming a locally linear n5ðB=cbÞ1=2 (3) conformation.11,17,24,30,31 Wavenumber q can be related to the correlation length, n, Significant questions regarding the local conformation and by q52p=n. The origin of this peak has been assigned to solubility of NaCMC in water thus remain unresolved. In this the inability of correlation blobs to overlap due to the strong work, we use small angle neutron scattering (SANS) to probe repulsion generated by the counterion clouds surrounding the solubility and conformation of NaCMC in aqueous solu- the polyions, thereby resulting in the suppression of long tion. We complement SANS results with careful steady shear range fluctuations.32,33 This is also manifested in the unusu- rheological measurements across a wide concentration range, ally low compressibility of polyelectrolyte solutions.34 which allows us to deduce the different concentration regimes and obtain further insight into the conformation and In the semidilute unentangled regime, the specific viscosity dynamics of NaCMC in water. of salt free polyelectrolyte solutions is given by:

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3 1=2 23=2 1 2J ðqr Þ gsp5Nðcb Þ B (4) 1 p 2 IðqÞhighq5I0 ð Þ 1Sinc (7) q qrp This power law dependence with c is usually referred to as 35 the Fuoss law, which has been observed for a number of The first term models the scattering of a wormlike chain

polyelectrolyte systems, although its validity has been ques- with a cross sectional radius rp. The constant I0 is a function 36,37 tioned. Equation 4 predicts the viscosity to depend line- of the contrast factor, the polymer concentration, and the

arly on N while, experimentally, it has been found that gsp monomer length (detailed in Supporting Information); J1 is a 222:4 37 / N for sodium polystyrene sulfonate (NaPSS), thus first-order Bessel function of the first kind, and the term Sinc suggesting the scaling argument might not be valid. However, accounts for the q-independent incoherent scattering. The the concentration dependences of both the viscosity and lon- (intermolecular) structure factor of polyelectrolyte solutions 38,39 gest relaxation time have been found experimentally and is complex to model48 and we, therefore, use an empirical 40 via simulations to agree with those expected from the approach by multiplying eq 7 by Rouse model, as has the experimentally measured relaxation 41 1 time distribution. HðqÞ5 (8) 12expð2ðqdÞm2kqÞ 4 Chains start to entangle at ce 5 n c*, where n is the number of overlapping chains necessary to form an entanglement. which yields a descriptive fit to the data from which the peak The tube diameter can be calculated to be a 5 nn and the position q,peakintensityIðqÞ, and a sharpness parameter reptation time and viscosity in semidilute entangled solu- can be extracted. We assign no physical meaning to the fitting tions are given by: parameters m, d,andk. Polyelectrolyte solutions exhibit a scattering upturn at low q values, with power laws between 2 3 22 3 23 49–55 32,33 srep5ðgsb =kBTÞn N B (5) and 4 which are not expected from scaling theory or PRISM.48 The origin of this upturn remains controver- 24 3 3 3=2 29=2 49,56,57 gsp5n N ðcb Þ B (6) sial, as it appears incompatible with the suppression of long range concentration fluctuations by the large osmotic The crossover concentration to the concentrated regime (cD) pressure created by counterions, which serves as a definition is expected when the correlation blob reaches the electrostatic of the correlation length in scaling theory.33 To complete our blob, that is nT 5 n. The chains are then predicted to behave fitting procedure, we include an additive power law term to 2n similarly to neutral polymers and the viscosity varies as gsp / eqs 7 and 8, IðqÞ5Dq and determine D and n as a function 3:75 14=3 42 c in good solvent and gsp / c in h solvents. These of concentration. A detailed account of this fitting procedure high exponents for the concentration dependence of the spe- is provided in Supporting Information. cific viscosity have been experimentally observed.38,43 For polyelectrolytes in poor solvent, there is no predicted exponent EXPERIMENTS but an even stronger concentration dependence may be expected as counterions condense to form ion pairs that NaCMC of average degree of substitution (D.S.) 1.15–1.45 attract each other. The terminal modulus is expected to scale and nominal Mw ’ 250 kg/mol was purchased from Sigma 2:3 as c for neutral polymers in good or h solvent. This scaling Aldrich. Aqueous GPC with elution solvent 0.3 M NaNO3/ is, however, not observed for concentrated polyelectrolyte sol- 0.002 M NaOH yields Mw 5 280 kg/mol and Mw=Mn53:4. utions,38,43 which are therefore rheologically distinct from The degree of substitution was measured by converting the neutral polymers. Scaling theory does not give a prediction for polymer into its acid form in a nitric acid-ethanol mixture, the existence of a peak in the scattering function in this adding a known amount NaOH and titrating the excess regime. Experimentally, it has been observed that for NaPSS, NaOH with HCl using phenolphthalein as an indicator, giving the scaling of the peak position with concentration changes D.S. 5 1.17 6 0.10. The residual salt in the polymer was cal- from 0.5 to 0.25, coinciding with a change in the scaling of culated by dialyzing a solution against DI water (using a 10 osmotic pressure with concentration, approaching a value sim- kDa Spectrapor membrane) and measuring the conductivity ilar to that of neutral polymers.34 A crossover to the 0.25 increase of the water. Using a totally dissolved solids conver- exponent has also been reported for less flexible polyelectro- sion factor of 0.6 mS/pmm, the salt content in the polymer is lytes poly(a-methylstyrene sulfonate), poly(diallyl dimethy- estimated to be ’ 0.4 wt %, in good agreement with the typ- lammonium chloride), and hyaluronic acid at intermediate ical purity of NaCMC samples (99.5 wt %). Water was concentrations, followed by a steeper power law of c1 at obtained from a MilliQ source and with resistivity of 18 MX/ 44,45 higher concentrations for the latter two. cm. D2O (99.8% D content) was purchased from Cambridge Isotopes. Rheological measurements were made on a stress controlled TA hybrid rheometer using a cone and plate Scattering geometry of diameter 40 or 60 mm and angle of 1 or 2,as We next consider the analysis and interpretation of SANS data well as an Anton Paar Physica MCR 301 using a double gap of NaCMC solutions in the semidilute and concentrated geometry, with internal and external gaps of 0.5 mm. regimes. The form factor of polyelectrolytes in solution can be described by a wormlike chain model. At high q, where we SANS experiments were carried out on three diffractometers: expect no intermolecular effects,46,47 the data are fitted with: time-of-flight SANS2D (ISIS, STFC, HSIC, Didcot, U.K.) with q-

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RESULTS

Rheology Figure 2 summarizes representative results of NaCMC solutions. We first obtain the zero shear rate viscosity (g0)fromthe Newtonian region of the profile and then fit the viscosity dependence of the shear rate to the Carreau model 2 p gðc_ Þ5g0=ð11ðsc_ Þ Þ ,wheregðc_ Þ is the dynamic viscosity of the solution, s [s] is a constant, which may be identified with the inverse of the shear rate at which shear thinning starts, p is an exponent which determines the power law of the viscosity with shear rate in the shear thinning regime and c_ [s21] is the shear rate. We also estimate the relaxation time from the inverse shear rate at which the viscosity reaches 90% of its zero shear rate value. For samples with gsp 10, inertial effects become important at high shear rates which lead to an appa- rent increase in the viscosity. We, therefore, consider only the Newtonian region below 100 s21, corresponding to the onset of inertial instabilities in water, and extract its Newtonian viscosity value. Figure 2(b) shows the specific viscosities (gsp)of NaCMC solutions as a function of concentration. The lines are the scaling predictions for the slopes of gsp for the semidilute unentangled (0.5), entangled (1.5) and concentrated regimes (3.75). These compare well to the best fit slopes 0.68 6 0.02,

1.7 6 0.2, and 3.4 6 0.3, respectively, and we identify ce to be ’ 2.9 g/L and cD ’ 14.4 g/L using the scaling theory power laws and ce 5 4 g/L and cD 5 14.3 g/L using the best fit power laws. Although our measurements do not extend to low enough concentrations to measure the overlap concentration c*, we can FIGURE 2 Rheology of NaCMC aqueous solutions. (a) Repre- obtain an estimate by extrapolating the unentangled data sentative rheograms for c 5 0.21 to 36 g/L, (b) specific viscosity (using the best fit 0.68 exponent) to gsp 5 1, which gives c as a function of concentration. The lines indicate the scaling ’ 0:07 g/L. The relaxation times in the 3–14 g/L range, within predictions for the semidilute unentangled, semidilute the semidilute entangled region as identified from viscosity, entangled and concentrated power laws. c) Relaxation times (s) remain constant within experimental error, in agreement with as a function of concentration, red ᭜ from Carreau model and eq 4. The relaxation times for concentrations above ’ 14 g/L blue • from shear rate at which viscosity is equal to 90% of its vary as c3:061, which is higher than the scaling prediction for zero shear value. Lines indicate power laws of 0 and 3. The entangled neutral polymers in both good (1.6) and h (2.3) sol- dotted vertical line indicates cD 5 14.4g/L. [Color figure can be viewed in the online issue, which is available at wileyonlineli- vents, but the uncertainty is large as the concentration is only brary.com.] varied by a factor of ’ 2 in this concentration regime.

We tested a high concentration (c 5 40 g/L) sample for thixot- features are observed, namely the presence of a correlation ropy by measuring its viscosity in the shear rate range of 1 to peak, whose position q increases with concentration, and 21 21 800 s before and after shearing for 2 min at 800 s .No the characteristic low q upturn discussed earlier. time dependence of the viscosity was observed, and we, therefore, assume that all the samples studied (c 40 g/L) are High q: The Chain Diameter nonthixotropic. The D11 and D22 profiles were fitted with eq 7. We find that more consistent results are obtained when fitting the Small angle neutron scattering range q > 1.5q, and representative fits are shown in Figure Figure 3 shows the scattering profiles for NaCMC solutions 4(a). A Gaussian, instead of step density, chain cross section with concentrations from 4 to 40 g/L. Typical polyelectrolyte profile gives similar values of rp. An alternative fitting

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A value of rp 5 3.4 Å, indicated by the dashed line in Figure 4(b) is selected and imposed on subsequent data fits for all

the samples, with I0 and Sinc now being the only free parameters. The model agreement with the data does not change

significantly compared to leaving rp as a free parameter. To ensure consistency, we evaluate the dependence of I0 and Sinc with concentration, as we expect Sinc to be proportional to /, the volume fraction occupied by monomers, and I0 to be proportional to /(1 2 /), both with intercept at the origin. This is confirmed with a linear regression correlation coefficient (R2) in the range of 0.99 to 0.93 for all datasets.

Comparing the value of I0 with the calculated one from the SLDs and partial molar volume of CMC,64 we estimate the water content in the samples to be ’ 14% for SANS 2D and ’ 19% for the D11 and D22 samples, the difference arising possibly due to slightly different drying conditions and small errors in the absolute calibration of the neutron data. All the concentrations in this article are reported using the cor- rected concentration (assuming the water content to be 18% for the rheology samples). The incoherent scattering of the pol 21 polymer is found to be Sinc ’ 0:4 6 0.1 cm .

FIGURE 3 Coherent SANS profiles for aqueous solutions of NaCMC for different concentrations ranging from 4 to 40 g/L, curves shifted in 53 increments for clarity. The 4 g/L curve is not shifted. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

procedure using a helical form factor,58 described in Sup- porting Information, yields an effective chain radius of 3.0 6 1.5 Å and linear mass density of the chain ’ 5% higher than the linear chain, such that these two descriptions are effectively very similar. We adopt the wormlike model throughout the article and comment on the (minor) differences for the helical case where appropriate. The wormlike chain model describes the higher concentrations well but becomes poorer for c 10 g/L, when an additional feature, a weak broad shoulder appears at high q. This feature has been observed in dilute solutions of NaPSS59 and semidilute solutions of tobacco mosaic virus,60 as well as in the small angle X-ray scattering (SAXS) of sodium alginate (in the concentration range of ’ 2–6g/L, although not discussed).61

More complex form factors, including the pearl necklace, elliptical cross section cylinder, two cylinders of different cross sections, the fraction and radii of which were left as free parameters, and single or double helix (pitch with an upper bound of ’ 200 Å) do not yield significantly better agreement than a single cylinder. Including the contribution of the counterions, as calculated by the Katchalsky cell model,47,62,63 also did not improve the fit. FIGURE 4 (a) Coherent SANS profiles for NaCMC solutions The rp values obtained from fitting the data with eq 7 are with concentrations: Blue ᭜ c 5 30 g/L, black ~ c 5 11 g/L, and plotted in Figure 4(b). The slight increase at low concentra- red ᭜ c 5 4 g/L. Black line: fit to q > 1.5q data using eq 7. (b) tions is possibly an artefact due to the scattering shoulder at Cylindrical chain radius as a function of concentration. Dashed ˚ lower concentrations. The values are approximately constant line indicates rp 5 3.4 A. [Color figure can be viewed in the for c 10 g/L. online issue, which is available at wileyonlinelibrary.com.]

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FIGURE 5 Sequence of fitting stages for 30 g/L aqueous solution of NaCMC. (a) Wormlike chain fit to high q data, shown in black; (b) the peak function (blue line) and the upturn, modeled as a power law fit (green line); (c) the overall fit to the data. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Intermediate and Low q-Ranges: Correlation Peak and ing Information; broadly we find that it increases with concen- Upturn tration for c 10g/L. Figure 5 shows the sequential stages of data fitting. First, a wormlike chain form factor with finite cross section, deter- DISCUSSION mined previously, is fitted to the high q data, indicated by Structure the black line. Then, we use eq 8 to fit the correlation peak Chain Diameter (blue line), and finally, we add an upturn term D/qn indi- The local conformation of a semiflexible polyelectrolyte is cated by the green line. We find that n 5 3.6 is close to the expected to be straight and a fit to a cylindrical form factor best fit slope for all samples and is thus fixed.

The peak position q and the intensity at the peak IðqÞ are plotted as functions of concentration in Figure 6. The best fit imposing a 0.5 power law is found for q 5 (0.021 6 0.003) c1=2 Å21. No change in the scaling of q with concentration is observed across cD, the concentrated crossover, (indicated by the change of blue to red data points). The best fit power law for all samples is IðqÞ/c0:4, similar to what has been observed for other systems in the semidilute regime and in reasonable agreement with the scaling prediction of IðqÞ/c0:5. Alternatively, IðqÞ can be fitted with a 0.5 power law for c 8g/L and a 0.3 slope for c 8g/L. A 12 g/L sam- plewasrunat5,25,45and65 C, and q was found to be insensitive to temperature within ’ 10% uncertainty.

Determining the peak width, for example as a full width half maximum parameter, is complex as it requires extrapolation into the region where the low q upturn dominates. We, therefore, compute the full width at 75% of its maximum value (i.e. 3IðqÞ/4, termed FW75M) as a measure of peak width, which yields consistent results. The peak sharpness, defined as IðqÞ= FW75M shows no trend with concentration and is approxi- FIGURE 6 Correlation peak intensity IðqÞ and position q as func- 8 mately constant at a value of (9.6 6 0.5) 10 (dimensionless). tions of concentration; blue symbols for samples in the semidilute The SANS2D data show slightly sharper peaks than those from regime and red for those in the concentrated. Numbers indicate D11 and D22, likely due to data reduction and/or a small pres- the slopes for the best fit single power law. The dotted lines indi- ence of ions in the D2O. The dependence of the low q upturn cate the cD as identified by rheology. [Color figure can be viewed intensity as a function of concentration is presented in Support- in the online issue, which is available at wileyonlinelibrary.com.]

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thus yields the cross sectional radius of the chain. The fit- Overlap Concentration 42 ted radius of rp 5 3.4 6 1.0 Å is lower than the one calcu- Estimating c from gspðc Þ51 is commonly used, although 17 lated from bond lengths 5 Å but higher than that found the definition is somewhat arbitrary as it assumes gsp 5 [g]c for sodium alginate,65 another polysaccharide, from SAXS. in the dilute regime, where [g] is the intrinsic viscosity, and The mass per unit length and chain diameter from a fit to c 5 1/[g]. We obtain c50.07 g/L from this method, which a single helix yields very similar results to the cylindrical we expect overestimates c as gspðc Þ < 1 has been found fit indicating that, if a helical conformation is present, its experimentally for NaPSS.69 We may also estimate c by effect on the local conformation is minor. The weak equating the experimentally measured correlation length to shoulder appearing in the lower concentration samples (c the end-to-end distance (nðc Þ5Ree) of chains at overlap and Շ 15 g/L) could not be fitted to any of the models we requiring that the chains occupy the whole volume of the attempted. It has been predicted by theory48 and verified solution (i.e., cnðcÞ3 5 1, where c is in units of chains per 50,60 by experiment, that the intermolecular structure factor unit volume), which is equivalent to eq 2 with Ree5nðc Þ. is not exactly equal to one at high q but shows small, This method gives c50:003 g/L. Calculating the volume

damped oscillations, which become less prominent with fraction occupied by the chains (/pol)atc 5 0.07 g/L assum- increasing concentration. It is thus possible that it arises ing the end-to-end distance of the chains to be n(0.07 g/L) from an intermolecular effect. ’ 1120 Å (calculated using the experimental relation 21=2 n 5 296 c ), yields /pol50:2, as opposed to the expected Correlation Length /polðc Þ’1, which appears to be a large difference. Repeat- Assuming B 5 1 (chain is rigid up to n), scaling theory pre- ing this calculation for a number of systems reported in the dicts n 5 286 c21=2, close to the measured value of 296 literature, we find the calculated volume fractions to range c21=2 with c in [g/L], which corresponds to B 5 1.06 6 0.10, between 0.17 and 1, which is detailed in Supporting Infor- as calculated from eq 3. Assuming a helical conformation, mation. Generally, we may expect that the calculation of the instead of a wormlike chain fit at high q, we obtain overlap from scattering would under predict c as it assumes B 5 1.12 6 0.10, which is effectively the same within experi- chains to be rigid above nT in dilute solution when, in fact, mental error. The B ’ 1 measured value, corresponding to chains in dilute solution are best described by a directed an isotropic mesh of locally rigid rods, supports a locally stiff random walk of electrostatic blobs, and hence partially conformation, instead of a collapsed conformation or a large coiled. We can, therefore, regard the scattering and viscosity (strongly coiling) helix as previously suggested.25,26 Scaling estimates of c as lower and upper bounds, respectively. theory also predicts IðqÞ to vary as c1=2 in the semidilute : 6 : regime, close to the observed dependence c0 42 0 10. Rheology Semidilute Unentangled Regime Equations 1 and 3 give B 5 1.06 and n ’ 6Å for poor sol- T The viscosity results for the unentangled region indicate a vent and s ðT2hÞ=T ’ 0:9, where A is calculated from power law of 0.68 6 0.02 with concentration, higher than the Manning’s theory66–68 and with b 5 5.15Å, the monomer predicted slope from scaling theory of 0.5. This exponent does size. For good solvent, nearly identical values are obtained, not appear to be universal for polyelectrolytes: NaPSS has indicating that both cases are compatible with our data. As been shown to scale as 0.35,37 poly(2-vinylpyrridine) quater- cellulose is insoluble in water, we expect NaCMC to fall in nized with different ionic groups and to different extents the poor solvent case. The same calculation using b5L , the K0 shows an exponent of 0.5.38,70 Other polymers show greater Kuhn length (’ 100Å), gives n ’ 30Å. n L has the fol- 36,71 T T K0 exponents which arise, at least in some cases, due to shear lowing physical interpretation: the chain is rigid up to L K0 thinning or residual salt.37 The higher 0.68 exponent may due to intrinsic stiffness and between n and n due to elec- T arise from intrinsic rigidity of the chain; scaling theory trostatic repulsion. This is equivalent to B 5 1. assumes that the total persistence length (lp) of chains is purely electrostatic and equal to the correlation length, that is, Comment on Clustering and Solubility lp 5 le 5 n, resulting in the end-to-end distance of the chain in While our data are insufficient to resolve the structure of semidilute solution varying as R c21=4. Considering the possible clusters (manifested by the low q-upturn), the high intrinsic rigidity of the chain (l0) results in a weaker variation and intermediate q data allow us to effectively determine the of R with concentration, and should thus lead to a higher expo- solubility of NaCMC in water: the linear variation of I0 with 2 nent in the viscosity (gsp cR for Rouse chains). /(1 2 /) suggests no concentration dependent aggregation. Further, the values for the correlation length, in excellent Figure 7 shows the specific viscosity of semidilute unen- agreement with the expected values for locally stiff chains, tangled solutions as a function of concentration. The solid line

also indicate that no significant aggregation occurs; if a frac- is the scaling prediction using eq 4 with N calculated from Mw tion of chains were aggregated, the number of effective and B 5 1, which over-predicts the viscosity values by a factor chains contributing to the polyion mesh would decrease, of 3.5. The best fit to the data corresponds to B 5 2.3, shown leading to a higher n. Our results unambiguously establish by the dashed line. Differences in B from SANS and rheology the full solubility of NaCMC (D.S. 5 1.2) in water at a molecu- have been reported previously.38,70,72 We have analyzed data 20 1:260:1 lar level. Further discussion of the low q upturn is provided published by Kastner et al. and found gsp / N for in the Supporting Information. unentangled salt free solutions of NaCMC in water of varying

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N 5 3500, which has the same value of Nb/B, that is, the same effective contour length. NaCMC appears to require a similar number of chain overlaps to form an entanglement despite the large differences in molecular architecture.

The power law in the concentrated regime of 3.4 6 0.2 is in agreement with the scaling prediction that concentrated polyelectrolyte solutions should behave similarly to concentrated neutral polymer solutions.

The crossover between the semidilute and concentrated regimes is predicted by scaling theory to happen when n5nT , but that should not apply to more rigid polyelectrolytes. From FIGURE 7 Viscosity in the semidilute unentangled and rheology we conclude cD 5 14.4g/L, and we estimate from our entangled regimes. Unentangled regime: the full line is com- SANS results, we estimate n(cD) ’ 80 Å, much larger than the puted from eq 4 with B 51 and N calculated using Mw. The estimated values of nT and of the order of the intrinsic Kuhn dotted line is a best fit line with exponent of 0.5, corresponding 17,18 length (LK052l0) reported in the literature for NaCMC. cD to B 5 2.3. Entangled regime: the full line corresponds to eq 6 is also much lower than that of flexible polyelectrolytes such with B 5 2.3 and n 5 3.2. [Color figure can be viewed in the as NaPSS,34,73 or sodium polyacrylate74 (c 1M,/ 0.3). online issue, which is available at wileyonlinelibrary.com.] D Similarly, low concentrations have been reported for salt free 43,75 D.S. (0.75–1.47), in better agreement with the scaling predic- xanthan or alginate solutions as well as poly (acrylamide- tion for flexible polyelectrolytes. We still expect the agreement co-sodium 2-acrylamido-2-methylpropanesulfonate) with 71 10% degree of sulfonation. The correlation between cD and between our data and eq 4 to be only qualitative as prefactors 23=2 are ignored in its derivation. We, therefore, consider the l0 (cD l0 ) is further addressed in Supporting Information. B 5 1.06 value from SANS to be a better estimate. 21=2 21=4 We do not observe a change from n / c to c at cD,as reported in other systems,45,73 or a decrease in the IðqÞ Semidilute Entangled and Concentrated Regimes power law with concentration. The concentration cD where The terminal modulus may be estimated as G ’ðg2gsÞ/s. entangled polyelectrolyte scaling of the viscosity gives way We note, however, that s (/ N3) is estimated from the onset to concentrated solution is indicated by dashed lines in Fig- of shear thinning and is likely to correspond to the high ure 6 and the power laws persist for q*andI(q*) above and 73 molecular weight fraction of the sample while the viscosity below cD. As the fraction of condensed counterions 24 corresponds to the weight average of the entire distribution. increases across cD for NaCMC and other systems, we take For polydisperse systems, as is often the case of natural the n / c21=2 scaling as evidence that the electronstatic blob polymers, this will result in G being underestimated. We find concept (n / A2=3 in poor solvent) does not apply here. 1:060:2 G c and about kBT/10 per chain, in disagreement with the scaling prediction of kBT per chain for unentangled CONCLUSIONS solutions and of G c1:5 for semidilute entangled solutions. Power laws between 0.2 to 1.5 and prefactors close to kBT We have studied aqueous solutions of carboxymethyl cellu- per chain have been found for various polyelectrolyte/sol- lose of average degree of substitution 1.2 in the semidilute vent systems.37,39,70 Given the above considerations, it is and concentrated regimes by rheology and SANS. Both our likely the kBT/10 value arises due to sample polydispersity. SANS and rheology results indicate that NaCMC D.S. 5 1.2 is molecularly dispersed in water. Rheologically, NaCMC shows The scaling prediction for the slope in the entangled regime similar behavior to other polyelectrolyte systems, with a (3/2) is in good agreement with our best fit slope of near Fuoss law in the semidilute unentangled regime and in 1.7 6 0.2. The number of chain overlaps on the scale of the good agreement with scaling predictions in the entangled tube diameter needed to form an entanglement strand n, can and concentrated regimes. Using SANS, we measure the cross 1=4 33 be estimated from n5ðce=c Þ . Using ce 5 2.9 g/L and our sectional radius of the chain to be ’ 3.4 Å. At low concentra- estimates of c , we calculate the number of entanglements tions, below ’15 g/L, a shoulder appears in the scattering per chain n, to be 5.5 using the c derived from scattering or function at high q, the origin of which could not be resolved n 5 2.6 using c obtained from viscosity; we regard these as but appears to be associated to an intermolecular effect. 1=2 33 upper and lower bounds for n. Using n5gspðceÞ , yields n ’ 3:523:9. Leaving n as a free parameter in eq 6, a best We measure the correlation length from the position of the fit to the data is obtained for n 5 3.2, shown by the solid peak in the scattering function, which is in good agreement line in Figure 7. Equation 5 gives values approximately three with scaling predictions (B 5 1.06, n / c21=2). Interestingly, times lower than eq 6 which can be expected due to the there is no change in the scaling of the peak position or inten- aforementioned polydispersity effect. This value may be com- sity at the crossover to the concentrated regime, contrary to pared with n ’ 426 (obtained from the best fit lines in Fig. that observed in other systems. This contrasts with a sharp 1=4 1=2 4 of ref. 37 using n5ðce=c Þ and n5gspðceÞ ) for NaPSS change in the viscosity scaling with concentration across cD.

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The crossover happens when n ’ LK0 and cannot be rational- 20 U. Kastner, H. Hoffmann, R. Donges, J. Hilbig, Colloids Surf. ized in terms of the overlap of electrostatic blobs and correla- A 1997, 123–124, 307–328. tion blobs, as predicted by scaling theory for flexible 21 S. Guillot, M. Delsanti, S. Desert, D. Langevin, Langmuir polyelectrolytes. Flexible polyelectrolyte scaling theory provides 2003, 19, 230–237. a good description of the concentration dependence of the vis- 22 K. Tam, C. Tiu, J. Non-Newtonian Fluid Mech. 1993, 46, cosity, relaxation times, and correlation length for salt free 275–288. aqueous NaCMC solutions. 23 E. H. deButts, J. A. Hudy, J. H. Elliott, Ind. Eng. Chem. 1957, 49, 94–98. 24 D. Truzzolillo, F. Bordi, C. Cametti, S. Sennato, Phys. Rev. E ACKNOWLEDGMENTS 2009, 79, 011804. We thank EPSRC and Unilever for financial support, ILL and 25 J. Wang, P. Somasundaran, J. Colloid Interface Sci. 2005, ISIS for beam time, and a Leverhulme visiting professorship to 291, 75 – 83. RHC. We also thank Alessandra Vitale for help with the D.S. 26 O. Biermann, PhD thesis, Molecular Dynamics Simulation determination experiments, Geraint Roberts (Unilever) for Study of Polyelectrolyte Adsorption on Cellulose Surfaces, assistance with the rheology measurements, Edo Boek (Impe- Dortmund University, Dortmund (Germany), 2002. rial) for access to the Anton Paar rheometer, and Jack F. Douglas 27 K. Nishida, A. Iwasaki, Kolloid Z. Z. Polym. 1973, 251, 136– 138. (NIST) for useful discussions. 28 K. Nishida, K. Nagumo, H. Watanabe, Colloid. Polym. Sci. 1975, 253, 502–503. REFERENCES AND NOTES 29 J.-S. Zhao, J.-H. Wang, W.-B. He, Y.-B. Ruan, Y.-B. Jiang, 1 D. Klemm, B. Philipp, T. Heinze, U. Heinze, W. Wagenknecht, Chem. Eur. J. 2012, 18, 3631–3636. Comprehensive Cellulose Chemistry; Wiley-VCH Verlag GmbH 30 D. Truzzolillo, C. Cametti, S. Sennato, Phys. Chem. Chem. & Co. KGaA, 2004; pp 1–7, http://onlinelibrary.wiley.com/book/ Phys. 2009, 11, 1780–1786. 10.1002/3527601929. 31 T. Nishio, Biophys. Chem. 1996, 57, 261–267. 2 L. Schulz, B. Seger, W. Burchard, Macromol. Chem. Phys. 32 P. De Gennes, P. Pincus, R. Velasco, F. Brochard, J. Phys. 2000, 201, 2008–2022. France 1976, 37, 1461–1473. 3 W. Burchard, Cellulose 2003, 10, 213–225. 33 A. V. Dobrynin, R. H. Colby, M. Rubinstein, Macromolecules 4 C. Clasen, W.-M. Kulicke, Prog. Polym. Sci. 2001, 26, 1839– 1995, 28, 1859–1871. 1919. 34 L. Wang, V. A. Bloomfield, Macromolecules 1990, 23, 804– 5 M. Edali, M. N. Esmail, G. H. Vatistas, J. Appl. Polym. Sci. 809. 2001, 79, 1787–1801. 35 R. M. Fuoss, U. P. Strauss, J. Polym. Sci., Part A: Polym. 6 T. Garlick, P. Miner, Low stringing toothpaste; US Patent Chem. 1948, 3, 246–263. 5,192,529, 1993. 36 K.-F. Lin, H.-L. Cheng, Macromolecules 2000, 33, 4961–4965. 7 Industrial Gums: Polysaccharides and Their Derivatives, J. 37 D. C. Boris, R. H. Colby, Macromolecules 1998, 31, 5746– BeMiller & R. Whistler (Eds.), Academic Press; 1993. 5755. 8 L. D. Francis, Soil anti-redeposition agents,their use and 38 S. Dou, R. H. Colby, J. Polym. Sci. Part B: Polym. Phys. detergent compositions containing same; US Patent 3,597,416, 2006, 44, 2001–2013. 1971. 39 S. Dou, R. H. Colby, Macromolecules 2008, 41, 6505–6510. 9 W.-M. Kulicke, U. Reinhardt, G. G. Fuller, O. Arendt, Rheol. 40 Q. Liao, J.-M. Y. Carrillo, A. V. Dobrynin, M. Rubinstein, Acta 1999, 38, 26–33. Macromolecules 2007, 40, 7671–7679. 10 J. Elliot, A. Ganz, Rheol. Acta 1974, 13, 670–674. 41 Y. Takahashi, S. Iio, N. Matsumoto, I. Noda, Polymer Inter- 11 C. W. Hoogendam, A. de Keizer, M. A. Cohen Stuart, B. H. national 1996, 40, 269–273. Bijsterbosch, J. A. M. Smit, J. A. P. P. van Dijk, P. M. 42 R. H. Colby, Rheol. Acta 2010, 49, 425–442. van der Horst, J. G. Batelaan, Macromolecules 1998, 31, 43 N. B. Wyatt, M. W. Liberatore, J. Appl. Polym. Sci. 2009, 6297–6309. 114, 4076–4084. 12 W. Brown, D. Henley, Makromol. Chem. 1964, 79, 68–88. 44 P. Lorchat, I. Konko, J. Combet, J. Jestin, A. Johner, A. 13 L. Xiquan, Q. Tingzhu, Q. Shaoqui, Acta Polym. 1990, 41, Laschewski, S. Obukhov, M. Rawiso, Europhys. Lett. 2014, 106, 220–222. 28003. 14 M. Dolz, J. Bugaj, J. Pellicer, M. Hernandez, M. Gorecki, J. 45 P. Lorchat, PhD Thesis, Structure des solutions aqueuses de Pharm. Sci. 1997, 86, 1283–1287. polyelectrolytes fortement charges, Institut Charles Sadron - 15 J. Reuben, H. Conner, Carbohydr. Res. 1983, 115, 1–13. Strasbourg (France) 2012. 16 A. Adden, PhD Thesis, Substitution Patterns in and over 46 K. Nishida, K. Kaji, T. Kanaya, T. Shibano, Macromolecules Polymer Chains New Approaches for Carboxymethyl Cellulose, 2002, 35, 4084–4089. Technischen Universitat Carolo-Wilhelmina, Hannover (Ger- 47 K. Kassapidou, W. Jesse, M. E. Kuil, A. Lapp, S. Egelhaaf, J. many), 2009. R. C. van der Maarel, Macromolecules 1997, 30, 2671–2684. 17 R. M. Davis, Macromolecules 1991, 24, 1149–1155. 48 A. Yethiraj, J. Phys. Chem. B 2009, 113, 1539–1551. 18 K. Kamide, M. Saito, H. Suzuki, Makromol. Chem. Rapid 49 Y. Zhang, J. F. Douglas, B. D. Ermi, E. J. Amis, J. Chem. Commum. 1983, 4, 33–39. Phys. 2001, 114, 3299–3313. 19 V. N. Tsvetkov, P. N. Lavrenko, S. V. Bushin, J. Polymer Sci. 50 M. Spiteri, Thesis, Conformation et corrrelations spatiales Polymer Chem. Ed. 1984, 22, 3447–3486. dans les solutions de polyelectrolytes: etude par Diffusion de

500 JOURNAL OF POLYMER SCIENCE, PART B: POLYMER PHYSICS 2015, 53, 492–501 JOURNAL OF POLYMER SCIENCE WWW.POLYMERPHYSICS.ORG FULL PAPER

Neutrons aux Petits Angles, Universite Orsay - Paris-Sud, 64 S. Koda, S. Hasegawa, M. Mikuriya, F. Kawaizumi, H. Orsay (France), 1997. Nomura, Polymer 1988, 29, 2100–2104. 51 B. D. Ermi, E. J. Amis, Macromolecules 1998, 31, 7378–7384. 65 Z.-Y. Wang, J. W. White, M. Konno, S. Saito, T. Nozawa, 52 P. Vallat, J.-M. Catala, M. Rawiso, F. Schosseler, Macromo- Biopolymers 1995, 35, 227–238. lecules 2007, 40, 3779–3783. 66 G. S. Manning, J. Chem. Phys. 1969, 51, 924–933. 53 E. Geissler, A.-M. Hecht, F. Horkay, Macromol. Symp. 2010, 67 A. V. Dobrynin, M. Rubinstein, Prog. Polym. Sci. 2005, 30, 291–292, 362–370. 1049–1118. 54 S. Popa-Nita, C. Rochas, L. David, A. Domard, Langmuir 68 F. Bordi, C. Cametti, R. H. Colby, J. Phys.: Condens. Matter 2009, 25, 6460–6468. 2004, 16, R1423. 55 F. Horkay, P. J. Basser, A.-M. Hecht, E. Geissler, Macromole- 69 J. Eckelt, A. Knopf, B. A. Wolf, Macromolecules 2008, 41, cules 2012, 45, 2882–2890. 912–918. 56 M. Sedlak, J. Chem. Phys. 1996, 105, 10123–10133. 70 W. E. Krause, J. S. Tan, R. H. Colby, J. Polym. Sci., Part B: Polym. Phys. 1999, 37, 3429–3437. 57 M. Sedlak, J. Chem. Phys. 2002, 116, 5256–5262. 71 P. Kujawa, A. Audibert-Hayet, J. Selb, F. Candau, J. Polym. 58 P. Szekely, A. Ginsburg, T. Ben-Nun, U. Raviv, Langmuir Sci. Part B: Polym. Phys. 2004, 42, 1640–1655. 2010, 26, 13110–13129. 72 E. Di Cola, N. Plucktaveesak, T. A. Waigh, R. H. Colby, J. S. € 59 R. Krause, E. Maier, M. Deggelmann, M. Hagenbuchle, S. Tan, W. Pyckhout-Hintzen, R. K. Heenan, Macromolecules 2004, Schulz, R. Weber, Physica A 1989, 160, 135–147. 37, 8457–8465. 60 E. E. Maier, R. Krause, M. Deggelmann, M. Hagenbuechle, 73 K. Nishida, K. Kaji, T. Kanaya, J. Chem. Phys. 2001, 114, R. Weber, S. Fraden, Macromolecules 1992, 25, 1125–1133. 8671–8677. 61 E. Josef, H. Bianco-Peled, Soft Matter 2012, 8, 9156–9165. 74 F. Bordi, R. Colby, C. Cametti, L. De Lorenzo, T. Gili, J. Phys. 62 J. Van Der Maarel, M. Mandel, G. Jannink, Europhys. Lett. Chem. B 2002, 106, 6887–6893. 1992, 20, 607–612. 75 C. Rodrıguez-Rivero, L. Hilliou, E. M. M. del Valle, M. A. 63 A. Katchalsky, Pure Appl. Chem 1971, 26, 327–373. Galan, Rheolog. Acta 2014, 53, 559–570.

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